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Proof-theoretic analysis of KPM

1991
*
Archive for Mathematical Logic
*

In this paper we show that a certain ordinal notation

doi:10.1007/bf01621475
fatcat:yxcbpnlu3nggpax47suqhvutni
*system*is sufficient to measure the*proof*-*theoretic*strength*of*KPM. ... KPM is a subsystem*of*set theory designed to formalize a recursively Mahlo universe*of*sets. ... I also profited from a "work-out"*of*[2] given by Ludwig Tautz. Thanks are due to Professor Pohlers for stimulating conversations about*proof*theory. ...##
###
Proof Theoretic Analysis by Iterated Reflection
[chapter]

2015
*
Turing's Revolution
*

We compare the information obtained by this kind

doi:10.1007/978-3-319-22156-4_9
fatcat:ogd5nz5h3vd23ef4fzfjcwqgdi
*of**analysis*with the results obtained by the more usual*proof*-*theoretic*techniques. ... It has to be noted, however, that the standard*proof*-*theoretic*methods, in practical cases, usually allow to define natural ordinal notation*systems*for suitable initial segments*of*the constructive ordinals ... Thus, the calculation*of**proof*-*theoretic*ordinals, or ordinal*analysis*, has become one*of*the central aims in the study*of*formal*systems*(cf. [22] ). ...##
###
Proof-theoretic analysis by iterated reflection

2003
*
Archive for Mathematical Logic
*

We compare the information obtained by this kind

doi:10.1007/s00153-002-0158-7
fatcat:4ivmz7xtgbhntd7khx6ostj23y
*of**analysis*with the results obtained by the more usual*proof*-*theoretic*techniques. ... It has to be noted, however, that the standard*proof*-*theoretic*methods, in practical cases, usually allow to define natural ordinal notation*systems*for suitable initial segments*of*the constructive ordinals ... Thus, the calculation*of**proof*-*theoretic*ordinals, or ordinal*analysis*, has become one*of*the central aims in the study*of*formal*systems*(cf. [22] ). ...##
###
Proof Theoretic Complexity
[chapter]

2002
*
Proof and System-Reliability
*

In particular, Leivant's (1995) theories based on his ramified induction schemes give

doi:10.1007/978-94-010-0413-8_12
fatcat:mo6ha6scmzckrljxoqfuqidsae
*proof**theoretic*characterizations*of*PTIME*and*the low Grzegorczyk*classes*E 2*and*E 3 . ... Previous results*of*Leivant are reworked*and*extended in this new setting, with quite different*proof**theoretic*methods. computable. ... It will be convenient, for later*proof**theoretic**analysis*, to work with logic in a sequent-style formalism,*and*the*system*G3 (with structural rules absorbed) as set out on page 65*of*Troelstra*and*Schwichtenberg ...##
###
A Game-Theoretic Computational Interpretation of Proofs in Classical Analysis
[article]

2012
*
arXiv
*
pre-print

It has been shown that a

arXiv:1204.5244v1
fatcat:d5joerlcgveehgdskqc6yfacuq
*functional*interpretation*of**proofs*in mathematical*analysis*can be given by the product*of*selection*functions*, a mode*of*recursion that has an intuitive reading in terms*of*the ... that can be clearly understood in game*theoretic*terms. ...*functionals**and*therefore exists in any model*of**system*T. ...##
###
Proof theory and computational analysis

1998
*
Electronical Notes in Theoretical Computer Science
*

In this survey paper we start with a discussion how

doi:10.1016/s1571-0661(05)80219-1
fatcat:ixrvz2n45jbjffobwhegqgyfxq
*functionals**of*nite type can be used for the*proof*-*theoretic*extraction*of*numerical data (e.g. e ective uniform bounds*and*rates*of*convergence) from ... non-constructive*proofs*in numerical*analysis*. ... So PB can be considered as a (very*weak*)*system**of*polynomially bounded arithmetic. ...##
###
Nonclassical truth with classical strength. A proof-theoretic analysis of compositional truth over HYPE
[article]

2020
*
arXiv
*
pre-print

Questions concerning the

arXiv:2007.07188v3
fatcat:s3r5tmrnhfbklh4xr3jngcdvdu
*proof*-*theoretic*strength*of*classical versus non-classical theories*of*truth have received some attention recently. ... A particularly convenient case study concerns classical*and*nonclassical axiomatizations*of*fixed-point semantics. ... then conclude that the*systems**of*ramified*analysis*below Γ 0 are*proof*-*theoretically*reducible to our*system*KFL * . ...##
###
The proof-theoretic analysis of Σ11 transfinite dependent choice

2003
*
Annals of Pure and Applied Logic
*

This article provides an ordinal

doi:10.1016/s0168-0072(03)00006-x
fatcat:sphmyymtrfbglklqmutfhhvldm
*analysis**of*1 1 transÿnite dependent choice. ... Finite reduction In this*and*the next section the*proof*-*theoretic**analysis**of*E n is given. ... The theory 1 1 -TDC 0*and*its*proof*-*theoretic**analysis*typically belong to the new area*of*so-called metapredicative*proof*theory. ...##
###
Proof-Theoretic Analysis of The Quantified Argument Calculus

2019
*
The Review of Symbolic Logic
*

this out. reason to use sequent calculus in this

doi:10.1017/s1755020318000114
fatcat:ke464pghrrhhdle4mrktac4d6y
*analysis*is to provide a constructive*proof**of*consistency, but first*and*foremost to prove an important, useful*and*interesting result*of*a cut elimination ... Ben-Yami makes use*of*natural deduction (Suppes-Lemmonstyle), we, however, have chosen a sequent calculus presentation, which allows for the*proofs**of*a multitude*of*significant meta-*theoretic*results ... Given that this is an interesting but not widely known*system*, we will present it here in considerable detail before proceeding with the*proof*-*theoretic**analysis**of*it. ...##
###
Proof-theoretic strengths of weak theories for positive inductive definitions
[article]

2018
*
arXiv
*
pre-print

In this paper the lightface Π^1_1-Comprehension axiom is shown to be

arXiv:1603.01342v7
fatcat:sddiwn2iunenlje3fjcsfeqmzi
*proof*-*theoretically*strong even over RCA_0^*,*and*we calibrate the*proof*-*theoretic*ordinals*of**weak*fragments*of*the theory ID_1*of*... Conjunctions*of*negative*and*positive formulas in the transfinite induction axiom*of*ID_1 are shown to be*weak*,*and*disjunctions are strong. ... Our*proof**of*Theorem 2.4 is based on an*analysis*through the operator controlled derivations due to W. Buchholz [3] . An ordinal notation*system*with the ψ-*function*also due to W. ...##
###
A proof-theoretic semantic analysis of dynamic epistemic logic

2014
*
Journal of Logic and Computation
*

The present paper provides an

doi:10.1093/logcom/exu063
fatcat:im7schyimraarauhbockei3dim
*analysis**of*the existing*proof**systems*for dynamic epistemic logic from the viewpoint*of**proof*-*theoretic*semantics. ... Then, we review some*of*the most significant proposals*of**proof**systems*for dynamic epistemic logics,*and*we critically reflect on them in the light*of*the previously introduced*proof*-*theoretic*semantic ... that will arise from the*proof*-*theoretic**analysis*. ...##
###
A Proof-Theoretic Analysis of Theories for Stratified Inductive Definitions
[chapter]

2015
*
Gentzen's Centenary
*

In this article we study subsystems SID ν

doi:10.1007/978-3-319-10103-3_15
fatcat:shpvcwbcc5anjlv27a4bqzcjnq
*of*the theory ID 1 in which fixed point induction is restricted to properly stratified formulas. ... Before turning to the*proof*-*theoretic**analysis**of*the*systems*H ν , we need some further auxiliary notions. ... P This finishes our*proof*-*theoretic**analysis**of*the theories SID ν . ...##
###
On Relating Theories: Proof-Theoretical Reduction
[chapter]

2019
*
Mathesis Universalis, Computability and Proof
*

The notion

doi:10.1007/978-3-030-20447-1_16
fatcat:loptt6g2jfbmtdczu2qypbk2vu
*of**proof*-*theoretical*or finitistic reduction*of*one theory to another has a long tradition. ... devised for the purpose*of*formalizing*and*presenting various chunks*of*mathematics. ... Both, the support*and*the hospitality*of*HIM, are gratefully acknowledged. ...##
###
Essence As A Modality: A Proof-Theoretic and Nominalist Analysis

2021
*
Philosophers' Imprint
*

This essay adapts recent developments in

doi:10.3998/phimp.3521354.0021.007
fatcat:xlukbv22xncnbdtuikwervpvfi
*proof*-*theoretic*semantics to provide a nominalist*analysis*for a variety*of*essentialist vocabularies. ... On this proposal, object-language essentialist vocabulary is mentioned in a*proof*-*theoretic*metalanguage that uses a vocabulary*of*explanation. ... I will mention two*classes**of*question left open by this*analysis*: The first concerns details*of*the underlying*proof**system*,*and*the second concerns the use*of*that*proof**system*to interpret talk*of*essence ...##
###
Proof-theoretic investigations on Kruskal's theorem

1993
*
Annals of Pure and Applied Logic
*

Rathjen, M.

doi:10.1016/0168-0072(93)90192-g
fatcat:3y5qaamjwvdo7hoqnlovuruy3y
*and*A. Weiermann,*Proof*-*theoretic*investigations on Kruskal's theorem, Annals*of*Pure*and*Applied Logic 60 (1993) 49-88. ... Weiermann Our paper gives a complete*proof*-*theoretic*characterization*of*Kruskal's theorem in terms*of*ordinal notation*systems*, subsystems*of*second-order arithmetic,*and*subsystems*of*Kripke-Platek set ... An ordinal notation*system*Firstly, we need some ordinal-*theoretic*background. Let On be the*class**of*ordinals. ...
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